PSI - Issue 44

Fabio Di Trapani et al. / Procedia Structural Integrity 44 (2023) 1696–1703 Di Trapani F., Sberna A.P., Marano G. / Structural Integrity Procedia 00 (2022) 000–000

1699

4

for an individual), the fitness function involves a penalty function, that fictitiously increases the fitness value for unfeasible individuals, as:

F C = +Π

(3)

where C is the cost function and Π the penalty function. In particular, considering that the cost per surface area of reinforced plasters is a constant, this can be calculated as the area (in m 2 ) of reinforced plasters intervention, so that:

rp n

1 i C A = = 

(4)

, rp i

where A rp,i is the area of the i-th reinforced wall. It is noteworthy observing that for each wall, the area is computed twice, as the GFRP plaster is applied on both sides. The penalty function is instead defined as:

, wf j k p A A = =     1 1 wf ws n n j

   

Π = ⋅ 

(5)

, ws k



where p is a magnification coefficient fictitiously increasing the weight, in terms of retrofitting costs of the walls that don’t achieve flexural and shear safety checks. In Eq. (5) A wf,j and A ws,k represent the areas of walls having a strength capacity/demand ratio lower than the one with respect to flexure and shear respectively.

3. Analysis and post-processing of results

3.1. Seismic analysis and safety checks

The feasibility of each tentative retrofitting configuration is assessed by performing an equivalent static seismic analysis. According to Eurocode 8, and Italian NTC 2018, the equivalent horizontal seismic load is evaluated as:

1 ( ) ( / ) b d F S T W g = ⋅

⋅

λ

(6)

where S d (T 1 ) is the design spectral acceleration, W is the total weight of the structure, g is the gravitational acceleration, and λ is a corrective factor that is 0.85 if T 1 ≤ 2·T c and the structure has more than two stories, or 1 otherwise, while the fundamental period ( T 1 ) is estimated as T 1 = 0.05·H 3/4 , where H is the total height of the building. The combination of seismic forces simultaneously acting in the two horizontal orthogonal directions (X and Z) is considered by performing 8 analyses, where the forces are applied alternatively as 100% in one direction and 30% in the perpendicular one.

M u -N interaction diagram

1000 1200 1400 1600

2 m

2 m

f d =1 MPa 0d =0.02 MPa R =1.75 3 m

3 m

200 400 600 800

V u (kN)

0 400 800 1200 1600 2000 2400 2800 N (kN) 0

( b)

(a)

Fig. 2 – Unreinforced and reinforced interaction diagrams for a sample wall: (a) Mu-N; b) Vu-N.